document.write( "Question 1043599: how many sides are there for a regular polygon whose each interior angle is 108 degree \n" ); document.write( "

Algebra.Com's Answer #658741 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "how many sides are there for a regular polygon whose each interior angle is 108 degree
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document.write( "Consider two neighbor vertices of the polygon.\r\n" );
document.write( "Connect them by segments with the center of the polygon.\r\n" );
document.write( "You will get an isosceles triangle with one vertex at the center of the polygon.\r\n" );
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document.write( "Then each angle of 108 degs will be bisected in two angles of 54 degs each.\r\n" );
document.write( "So the angle at the base of your isosceles triangle is 54 degs.\r\n" );
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document.write( "Then the angle of the triangle at the center of the polygon is (180 - 2*54) = 72 degs.\r\n" );
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document.write( "To find the number of sides of the polygon, divide 360 degs by 72:  = 5.\r\n" );
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document.write( "Your polygon is a pentagon.\r\n" );
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